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Average CM-values of higher Green's function and factorization
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 144, Number 5, October 2022
- pp. 1241-1298
- 10.1353/ajm.2022.0029
- Article
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Abstract
abstract:
In this paper, we prove an averaged version of an algebraicity conjecture of Gross and Zagier concerning the values of higher Green's function at CM points. Furthermore, we give the factorization of the ideal generated by such algebraic value in the spirit of the famous work of Gross and Zagier on singular moduli.
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